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Macaulay2Doc :: groebnerBasis

groebnerBasis -- Gröbner basis, as a matrix

Synopsis

Description

i1 : R = QQ[a..d]

o1 = R

o1 : PolynomialRing
i2 : transpose groebnerBasis random(R^1,R^{4:-2})

o2 = {-2} | 57607935ac-36934002bc+1742137980c2+130132660ad+115901037bd+936394
     {-2} | 1382590440b2+912043062bc-813567876c2+620658913ad+351451653bd+1596
     {-2} | 6982780ab-540624bc-7971384c2-1644013ad-467124bd-110460cd-33145d2 
     {-2} | 2244465a2+441000bc-4329384c2+229957ad-160566bd+461160cd+18900d2  
     {-3} | 733357674860797587851282099498602440576c2d+4059420094647520120496
     {-3} | 1100036512291196381776923149247903660864bcd+156030470425065045826
     {-3} | 11000365122911963817769231492479036608640c3-695812268099405097648
     {-3} | 2200073024582392763553846298495807321728bc2-734631449404213174992
     {-4} | 29629483832144617807968030117887645638298209270712665301402447722
     {-4} | 29629483832144617807968030117887645638298209270712665301402447722
     {-4} | 98764946107148726026560100392958818794327364235708884338008159076
     {-5} | d5                                                               
     ------------------------------------------------------------------------
     20cd+35346045d2                                                         
     922320cd+1119303675d2                                                   
                                                                             
                                                                             
     1297290110674317ad2+51329070872061317905520211045757602623bd2+2798624117
     739370729548063635ad2+146582550547275925694917351064470193057bd2-1373712
     046251346624952665ad2-123100411025819316928742873474625680539bd2+1386264
     91736736473484115ad2-9880070667480091688841941954361300113bd2-7033572036
     966017cd3+59619041477489880307552320403353384834884800099551860237435003
     966017bd3+42772445394156610220296267656317536468181984823465710724875189
     55339ad3+145880255137080659693688985637603435992332848233148843916545162
                                                                             
     ------------------------------------------------------------------------
                                                                             
                                                                             
                                                                             
                                                                             
     6796538683613228656207656015cd2+11604455650709397491025599094486141560d3
     170673425558543236072481238177295cd2-30814841450096732222656126502481187
     161329965291729724817802697400645cd2+22291608910332870879516604536071881
     3446872736009053838628396545cd2-106260636146112180792715552389896297720d
     73903209d4                                                              
     815443700d4                                                             
     8205683d4                                                               
                                                                             
     ------------------------------------------------------------------------
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     5160d3 |
     0880d3 |
     3      |
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             12       1
o2 : Matrix R   <--- R